It's written in the detailed spoiler.
In Onigashima's dome, Kaidou murmurs that he saw Oden's shadow in the Red Scabbards' attack. But as he thought, the Red Scabbards are not Oden.
Kaidou: "I would have been fine with letting myself killed.
There will never be any samurai as strong as Oden!
Your power isn't enough to kill me!!"
Then he gets pissed and takes Kiku's arm clean off, casually as fuck.